Browsing by Author "HonChung, Man"

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    Computing an optimal hatching direction in Layered Manufacturing
    (2001-02-01) Schwerdt, Jörg; Smid, Michiel; HonChung, Man; Janardan, Ravi
    In Layered manufacturing (LM), a prototype of a virtual polyhedral object is built by slicing the object into polygonal layers, and then building the layers one after another. In StereoLithography, a specific LM-technology, a layer is built using a laser which follows paths along equally-spaced parallel lines and hatches all segments on these lines that are contained in the layer. We consider the problem of computing a direction of these lines for which the number of segments to be hatched is minimum, and present an algorithm that solves this problem exactly. The algorithm has been implemented and experimental results are reported for real-world polyhedral models obtained from industry.
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    Minimizing the total projection of a set of vectors, with applications to Layered Manufacturing
    (2001-02-01) HonChung, Man; Janardan, Ravi; Schwerdt, Jörg; Smid, Michiel
    In Layered manufacturing, a three-dimensional polyhedral solid is built as a stack of two-dimensional slices. Each slice (a polygon) is built by filling its interior with a sequence of parallel line segments (of some small non-zero width), in a process called hatching. A critical step in hatching is choosing a direction which minimizes the number of segments. In this paper, this problem is approximated as the problem of finding a direction which minimizes the total projected length of a certain set of vectors. Efficient algorithms are proposed for the latter problem, using techniques from computational geometry. Experimental and theoretical analyses show that this approach yields results that approximate closely the optimal solution to the hatching problem of finding a direction which minimizes the total projected length of a certain set of vectors. Efficient algorithms are proposed for the latter problem, using techniques from computational geometry. Experimental and theoretical analyses show that this approach yields results that approximate closely the optimal solution to the hatching problem. Extensions of these results to several related problems are also discussed.